Answer
$\{(5,1)\}$
Work Step by Step
Use Gauss-Jordan to perform the row operations given, we have:
$\begin{bmatrix} 3 & -2 & 13 \\ 4 & -1 & 19 \end{bmatrix} \begin{array} .\\3R2-4R1\to R2\\ \end{array}$
$\begin{bmatrix} 3 & -2 & 13 \\ 0 & 5 & 5 \end{bmatrix} \begin{array} .\\R2/5\to R2\\ \end{array}$
$\begin{bmatrix} 3 & -2 & 13 \\ 0 & 1 & 1 \end{bmatrix} \begin{array} .R1+2R2\to R1\\.\\ \end{array}$
$\begin{bmatrix} 3 & 0 & 15 \\ 0 & 1 & 1 \end{bmatrix} \begin{array} .R1/3\to R1\\.\\ \end{array}$
$\begin{bmatrix} 1 & 0 & 5 \\ 0 & 1 & 1 \end{bmatrix} \begin{array} .\\.\\ \end{array}$
Thus the solution set is $\{(5,1)\}$
